- 1,682

- 50

- Problem Statement
- Give an example of a function ##u## such that ##u:I\to I=(−1,1)## such that ##|u(x)−u(y)|\leq 0.5|x−y|## for all ##x,y\in I##, and ##u(x) \neq x## for all ##x\in I##.

- Relevant Equations
- Nothing comes to mind

Well doesn't ##u(x) = 0.4 x## work? Seems too easy, but the phrasing at the end "for all ##x\in I##" makes me think since ##0.4x = x## only at ##x=0##, and not all of ##I##, that this is okay. But am I wrong?